Cost of capital

Fianancial Management & international finance66
COST-VOLUME-PROFIT ANALYSISFinancial Management Decisions
2.2 Cost Of Capital
INTRODUCTION:
It has been discussed in lesson -4 that for evaluating capital investment proposals according to
the sophisticated techniques like Net Present Value and Internal Rate of Return, the criterion
used to accept or reject a proposal is the cost of capital. The cost of capital plays a significant
role in capital budgeting decisions. In the present lesson the concept of cost of capital and the
methods for its computation are explained.
COST OF CAPITAL-KEY CONCEPTS:
The term cost of capital refers to the minimum rate of return a firm must earn on its invest-
ments. This is in consonance with the firm’s overall object of wealth maximization. Cost of
capital is a complex, controversial but significant concept in financial management.
The following definitions give clarity management.
Hamption J.: The cost of capital may be defined as “the rate of return the firm requires from
investment in order to increase the value of the firm in the market place”.
James C. Van Horne: The cost of capital is “a cut-off rate for the allocation of capital to invest-
ments of projects. It is the rate of return on a project that will leave unchanged the market price
of the stock”.
Soloman Ezra:”Cost of Capital is the minimum required rate of earinings or the cut-off rate of
capital expenditure”.
It is clear from the above difinitions that the cast of capital is that minimum rate of return
which a firm is expected to earn on its investments so that the market value of its share is
maintained. We can also conclude from the above definitions that there are three basic aspects
of the concept of cost of capital:
i) Not a cost as such: In fast the cost of capital is not a cost as such, it is the rate of return
that a firm requires to earn from its projects.
ii) It is the minimum rate of return: A firm’s cost of capital is that minimum rate of
return which will at least maintain the market value of the share.
iii) It comprises three components:
This Section includes :
••••• Cost of Capital-Key Concepts
••••• Importance
••••• Classification
••••• Determination of Cost of Capital
••••• Computation
••••• Weighted Average Cost of Capital

67Fianancial Management & international finance
K=ro
+b+f
Where, k=cost of capital;
ro
= return at zero risk level:
b = premium for business risk, which refers to the variability in operating profit (EBIT) due to
change in sales.
f = premium for financial risk which is related to the pattern of capital structure.
IMPORTANCE OF COST OF CAPITAL:
The cost of capital is very important in financial management and plays a crucial role in the
following areas:
i) Capital budgeting decisions: The cost of capital is used for discounting cash flows
under Net Present Value method for investment proposals. So, it is very useful in
capital budgeting decisions.
ii) Capital structure decisions: An optimal capital is that structure at which the value
of the firm is Value of the firm is maximum and cost of capital is the lowest. So, cost
of capital is crucial in designing optimal capital structure.
iii) Evaluation of final Performance: Cost of capital is used to evaluate the financial
performance of top management. The actual profitabily is compared to the ex-
pected and actual cost of capital of funds and if profit is greater than the cast of
capital the performance nay be said to be satisfactory.
iv) Other financial decisions: Cost of capital is also useful in making such other finan-
cial decisions as dividend policy, capitalization of profits, making the rights issue,
etc.
CLASSIFICATION OF COST OF CAPITAL:
Cost of capital can be classified as follows:
i) Historical Cost and future Cost: Historical costs are book costs relating to the past,
while future costs are estimated costs act as guide for estimation of future costs.
ii) Specific Costs and Composite Costs: Specific accost is the cost if a specific source
of capital, while composite cost is combined cost of various sources of capital. Com-
posite cost, also known as the weighted average cost of capital, should be consid-
ered in capital and capital budgeting decisions.
iii) Explicit and Implicit Cost: Explicit cost of any source of finance is the discount
rate which equates the present value of cash inflows with the present value of cash
outflows. It is the internal rate of return and is calculated with the following for-
mula;

1 2 n
O 1 2 n
C C C
I .......
(I K) (I K) (I K)
= + + +
+ + +
Io
= Net cash inflow received at zero of time
C = Cash outflows in the period concerned
K = Explicit cost of capital
N = Duration of time period
Implicit cost also known as the opportunity cost is the of the opportunity foregone in order to
take up a particular project. For example, the implicit cast of retained earings is the rate of
return available to shareholders by investing the funds elsewhere.
iv) Average Cost and Marginal Cost: An average cost is the combined cost or weighted
average cost of various sources of capital. Marginal cost of refers to the average cost of
capital of new or additional funds required by a firm. It is the marginal cost which should
be taken into consideration in investment decisions.
DETERMINATION OF CAST OF CAPITAL :
As stated already, cost of capital plays a very important role in making decisions relating to
financial management. It involves the following problems.
Problems in determination of cost of capital:
i) Conceptual controversy regarding the relationship between cost of capital and capital
structure is a big problem.
ii) Controversy regarding the relevance or otherwise of historic costs pr future costs in
decision making process.
iii) ReeComputation of cost of equity capital depends upon the excepted rate of return
by its investors. But the quantification of expectations of equity shareholders is a
very difficult task.
iv) Retained earnings has the opportunity cost of dividends forgone by the sharehold-
ers. Since different shareholders may have different opportunities for reinvesting
dividends, it is very difficult to compute cost of retained earnings.
v) Whether to use book value or market value weights in determining weighted aver-
age cost of capital poses another problem.
COMPUTATION OF COST OF CAPITAL:
Computation of cost capital of a firm involves the following steps:
i) Computation of cost of specific sources of a capital, viz., debt, preference capital,
equity and retained earnings, and

ii) Computation of weighted average cost of capital.
Cost of Debt (kd
)
Debt may be perpetual or redeemable debt. Moreover, it may be issued at par,at premium or
discount. The computation of cost debt in each is explained below.
Perpetual / irredeemable debt:
i) At par:
Kd
= Cost of debt before tax =I/Po
Kd
= Cost of debt; I= interest; Po
= net proceeds
kd
(after-tax) = i/P(I-t)
Where T = tax rate
Example
Y Ltd issued Rs. 2,00,000, 9% debentures at a premium of 10%. The costs of floatation are 2% .
The tax rate is 50%. Compute the after tax cost of debt.
I Rs. 18,000
Answer: kd
(after-tax)= (i-t) (I-5)=4.17%
NP Rs. 2,15,600
[net proceeds = Rs. 2,00,000 + 20,000 – (2/100x2,20,000)]
Redeemable debt
The debt repayable after a certain period is known ad redeemable debt. Its cost computed by
using the following formula:
I+1/n (P-NP)
i) Before – tax cost of debt =
½ (P+NP)
I = interest: P= proceeds at par;
NP = net proceeds; n = No. of years in which debt is to be redeemed
ii) After tax of debt = Before – tax cost of debt x(1-t)
Example
A company issued Rs. 1,00,000 10% redeemble debentures at a discount of 50%. The cost of
floatation amount to Rs. 3,000. The debentures are redeemable after 5 years. Compute before
– tax and after – tax Cost of debt. The rate is 50%.

Solution :
I+1/n (P-NP)
i) Before – tax cost of debt =
½ (P+NP)
10,000+1/5(1,00,000-92,000)
=
½ (1,00,000+92,000)
10,000-16000 11,000
= = =12.08%
96,000 96,000
[NP=1,00,000 – 5,000 – 3,000=92,000]
After tax cost of debt = Before – tax cost x (1-t)=12.08X(1-.5)=6.04%
Cost of preference Capital(kP
)
In case of preference share dividend are payable at a fixed rate. However, the dividends are
not allowed to be deducted for computation of tax. So no adjustment for tax is required just
like debentures, preference share may be perpetual or redeemable. Future, they may be is-
sued at par, premium or discount.
Perpetual preference Capital
i) If issued at par ; Kp
= D/P
Kp
= Cost of preference capital
D = Annual preference dividend
P = Proceeds at par value
ii) If issued at premium or discount
Kp
= D/NP Where NP = net proceeds.
Example:
A company issued 10,000, 10% preference share of Rs. 10 each, Cost of issue is Rs. 2 per share.
Calculate cost of capital, of these shares are not issued (a) at par , (b) at 10% premium, and (c)
at 5% discount.
Solutions : Cost of preference capital, (Kp
) = D/NP
a) When issued at par:
Rs. 10,000 10,000
Kp
= x100 = x100 =12.5%
1,00,000-20,000 80,000
[ Cost of issued = 10,000xRs. 2= Rs. 20,000]

b) When issued at 10% premium:
Rs. 10,000 10,000
Kp
= x100 = x100 =11.11%
1,00,000 + 10,000-20,000 90,000
c) When issued at 5% discount:
Rs. 10,000 10,000
Kp
= x100 = x100 =13.33%
1,00,000- 5,000-20,000 75,000
Redeemable preference shares - It is calculated with the following formula:
D+ MV- NP/n
KP
=
½ (MV+NP)
Where, Kp
= Cost of preference capital
D = Annual preference dividend
MV = Maturity value of preference shares
NP = Net proceeds of preference shares
Example:
A company issues 1,00,000 10% preference share of Es. 10 each. Calculate the cost of prefer-
ence capital if it is redeemable after 10 years.
a) At par b) at 5% premium
Solution
D + 1/n MV- NP
KP
= ×100
½ (MV+NP)
a) Cost of preference capital , if redeemable at par:
Rs. 1,00,000 +1/10 (10,00,000 – 10,00,00) Rs. 1,00,000
KP
= x100 x100 = 10%
½ (10,00,000 +10,00,000) Rs. 10,00,000
b) If redeemable at a premium of 5% Kp
=
Rs. 1,00,000 +1/10 (10,50,000 – 10,00,00)
KP
= x100
½ (10,50,000 +10,00,000)
Rs. 1,00,000 + 5,000 Rs. 1,05,000
= X100 x100 = 10.24%
Rs. 10,25,000 Rs. 10,25,000

Cost of Equity capital
Cost of Equity is the expected rate of return by the equity shareholders. Some argue that, as
there is no legal for payment, equity capital does not involve any cost. But it is not correct.
Equity shareholders normally expect some dividend from the company while making invest-
ment in shares. Thus, the rate of return expected by them becomes the cost of equity. Concep-
tually, cost of equity share capital may be defined as the minimum rate of return that a firm
must earn on the equity part of total investment in a project in order to leave unchanged the
market price of such shares. For the determination of cost equity capital it may be divided into
two categories:
i) External equity or new issue of equity shares.
ii) Retained earnings.
The cost of external equity can be computed as per the following approaches:
Dividend Yield / Dividend Price Approach-According to this approach, the cost of equity will
be that rate of expected dividends which will maintain the present market price of equity
shares. It is calculated with the following formula:
Ke = D/NP (for new equity shares)
Or
Ke = D/MP (for existing shares)
Where,
Ke = Cost of equity
D = Expected dividend per share
NP = Net proceeds per share
Mp = Market price per share
This approach rightly recognizes the importance of dividends. However, it ignores the
importance of retained earnings on the market price of equity shares. This method is suitable
only when the company has stable earnings and stable dividend policy over a period of time.
Example
A company issues, 10,000 equity shares of Rs. 100 each at a premium of 10%. The company has
been paying 20% dividend to equity shareholders for the past five years and expected to main-
tain the same in the future also. Compute cost of equity capital. Will it make any difference if
the market price of equity share is Rs. 150 ?

Solution :
%18.18100
110.
20.
=×==
Rs
Rs
NP
D
Ke
If the market price per share =Rs.150
%33.13100
150.
20.
=×==
Rs
Rs
MP
D
Ke
Dividend yield plus Growth in dividend methods
According to this method, the cost of equity is determined on the basis if the expected divi-
dend rate plus the rate of growth in dividend. This method is used when dividends are ex-
pected to grow at a constant rate.
Cost of equity is calculated as:
Ke = D1
/NP +g (for new equity issue)
Where,
D1
= expected dividend per share at the end of the year. [D1
= Do
(1+g)]
Np = net proceeds per share
g = growth in dividend for existing share is calculated as:
D1
/ MP + g
Where,
MP = market price per share.
Example:
ABC Ltd plans to issued 1,00,000 new equity share of Rs. 10 each at par. The floatation costs
are expected to be 5% of the share price. The company pays a dividend of Rs. 1 per share and
the growth rate in dividend is expected to be 5%. Compute the cost of new issue share.
If the current the cost of new issue of shares.
Solution :
Cost of new equity shares = (Ke
) = D/NP +g
Ke
= 1 / (10-5-) + 0.05 = 1 / 9.5 + 0.05
= 0.01053 + 0.05
= 0.1553 or 15.53%
Cost of existing equity share: ke
= D / MP + g
Ke
= 1/ Rs. 15 = 0.05 = 0.0667 or 11.67%

Earnings Yield Method - According to this approach, the cost of equity is the discount rate
that capitalizes a stream of future earnings to evaluate the shareholdings. It is called by taking
earnings per share (EPS) into consideration. It is calculated as:
i) Ke
= Earnings per share / Net proceeds = EPS / NP [For new share]
ii) Ke
= EPS / MP [ For existing equity]
Example
XYZ Ltd is planning for an expenditure of Rs. 120 lakhs for its expansion programme. Number
of existing equity shares are 20 lakhs and the market value of equity shares is Rs. 60. It has net
earnings of Rs. 180 lakhs.
Compute the cost of existing equity share and the cost of equity capital assuming that new
share will be issued at a price of Rs. 52 per share and the costs of new issue will be Rs. 2 per
share.
Solutions
a) Cost of existing equity =
MP
EPS
Ke =)(
b) Earnings per share (EPS) = 9.
000,00,20
000,00,80,1
Rs=
Ke
=9/60=0.15 or 15%
c) Cost of new equity capital (Ke)
=ESP/NP=9/52-2=9/50=0.18 or 18%
Cost of Retained Earnings (Kr
)
Retained earnings refer to undistributed profits of a firm. Out of the total earnings, firms
generally distribute only past of them in the form of dividends and the rest will be retained
within the firms. Since no dividend is required to paid on retained earnings, it is stated that
‘retained earnings carry no cost’. But this approach is not appropriate. Retained earnings has
the opportunity cost of dividends in alternative investment becomes cost if retained earnings.
Hence, shareholders expect a return on retained earnings at least equity.
Kr
= Ke
= D/NP+g
However, while calculating cost of retained earnings, two adjustments should be made:
a) Income-tax adjustment as the shareholders are to pay some income tax out of dividends,
and b) adjustment for brokerage cost as the shareholders should incur some brokerage cost
while investment dividend income. Therefore, after these adjustments, cost of retained earn-
ings is calculated as:
Kr
= Ke
(1-t)(1-b)

Where, Kr
= cost of retained earnings
Ke
= Cost of equity
t = rate of tax
b = cost of purchasing new securities or brokerage cost.
Example
A firm ‘s cost of equity (Ke
) is 18%, the average income tax rate of shareholders is 30% and
brokerage cost of 2% is excepted to be incurred while investing their dividends in alternative
securities. Compute the cost of retained earnings.
Solution : Cost of retained earnings = (Kr
) = Ke
(1-t)(1-b)=18(1-.30)(1-.02)
=18x.7x.98=12.35%
Cost of Rights Issue
Rights issue is an invitation to the existing shareholders to subscribe for further shares to be
issued by a company. A right simply means an option to buy certain shares at a privileged
price which is considerably below the market price. It is generally felt that the cost of issue
would be different from the cost of direct issue. But for two reasons, the real cost of rights issue
would be the same as the cost of direct issue of share to the public.
i) The shareholder who is not interested in the rights issue, sells his rights and obtain
cash. Then he has the old share plus the money obtained from selling the rights.
ii) Otherwise, the shareholder exercise his rights and acquires the share the new share,
in addition to the old shares.
Thus, the present wealth of the shareholders in both the cases remains the same.
Cost of Convertible Securities
Convertible securities or debentures are another type of instruments for mobilization of debt
capital. In this case the debenture holder is entitled to gull pr a part of the value of the deben-
ture being converted into equity shares. The price at whch the debenture is convertible into
share is known as “conversion price”. This conversion price is declares at the time of the issue
of debentures itself.
When the bondholder exercises his option of conversion, he enjoys two benefits-interest on
bonds till the date of conversion and increased market value share a at the time of conversion.
Hence, the cost of convertible securities is taken to be that rate of discount swhich equates the
after-tax interest and the expected market value of the share at the end option period, with the
current market value of bond.
This is calculated with the help of following formula:
Po
=∑
Where,
Po
= Current market value of debenture
I = Interest
t = tax rate
Ko
= Rate of discount or cost of convertible security.
n = no. of years at the end of which conversion takes place.
CR = conversion or the no. of share the bond – holder gets on conversion

WEIGHTED AVERAGE COST OF CAPITAL :
It is the average of the costs of various sources of financing. It is also known as composite or
overall or average cost of capital.
After computing the cost of individual sources of finance, the weighted average cost of capital
is calculated by putting weights in the proportion of the various sources of funds to the total
funds.
Weighted average cost of capital is computed by using either of the following two types of
weights:
1) Market value 2) Book Value
Market value weights are sometimes preferred to the book value weights as the market value
represents the true value of the investors. However, market value weights suffer from the
following limitations:
i) Market value are subject to frequent fluctuations.
ii) Equity capital gets more importance, with the use of market value weights.
Moreover, book values are readily available.
Average cost of capital is computed as followings:
Kw =
Kw
w
Σ
Σ
Where, Kw = weighted average cost of capital
X = cost of specific sources of finance
W = weights (proportions of specific sources of finance in the total)
The following steps are involved in the computation of weighted average cost of capital :
i) Multiply the cost of each sources with the corresponding weight.
ii) Add all these weighted costs so that weighted average cost of capital is obtained.

Cost of capital

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